Question

An ideal gas expands quasi-statically and isothermally from a state with pressure p and volume V to a state with volume 4V. Show that the work done by the gas in the expansion is pV(ln 4).

Answer 1

The work done by the gas in the isothermal expansion is pV(ln 4).

Step-by-step explanation:

To show that the work done by the gas in the expansion is pV(ln 4), we can use the equation for work done by an ideal gas during an isothermal process:

W = nRT ln(Vf/Vi), where W is the work done, n is the number of moles of gas, R is the gas constant, T is the temperature in Kelvin, and Vi and Vf are the initial and final volumes respectively.

In this case, since the gas expands quasi-statically and isothermally, the temperature remains constant. Therefore, we can simplify the equation to:

W = nRT ln(Vf/Vi) = pV ln(Vf/Vi), where p is the pressure and V is the volume of the gas.

Using Vf = 4V and Vi = V, we can substitute these values into the equation:

W = pV ln(4V/V) = pV ln(4).